This is hardly a new misconception, in reality it's something the church has been dealing with its entire life. As Paul made his missionary journeys around the ancient world, preaching freedom from the Law of Moses, a group of ex-pharisees(known loosely as the Judaisers) would follow a few days behind him, preaching that Gentiles had to become Jews before they could become Christians. This teaching included circumcision, a kosher lifestyle, and generally following Mosaic Law. When Peter heard of this, he came before the Christian sect of the Pharisees, saying:

"...Brothers, you know that in the early days God chose me to be the one among you through whom the Gentiles would hear the message of the gospel and believe.
8 God, who knows everyone's heart, showed them he approved by giving them the Holy Spirit, just as he did to us. 9 He made no distinction between them and us, because he cleansed their hearts by faith. 10 So why do you test God by putting on the disciples' neck a yoke that neither our ancestors nor we could carry? 11 We certainly believe that it is through the grace of the Lord Jesus Christ that we are saved, just as they are."
--Acts 15:7b-11

The Mosaic law was difficult to follow to the letter. Many times, however, these difficulties arose from how the Pharisees and Saducees interpreted the law. These men were not only the Clergy, but also the Legislative, Executive, and on occasion the Judicial branches of their entire political system. If someone wanted to know if it was kosher to tie a certain type of knot on a certain day, they'd ask one of them (they're also referred to as Lawyers). If someone had a complaint against his neighbor, they'd bring it up with them. This eventually led to a very large, complex system which (by Peter's own admission) was impossible to follow.

For example, in dispensational circles it is argued that the law and the new covenant are distinct and unrelated dispensations of God's grace, and therefore the old covenant law is not binding upon partakers of the new covenant.

If you have more of a covenantal theology, then you must be very careful before flatly dismissing adherence to the law, because the new covenant builds upon (instead of replaces) the old. Those who would say at least part of the OT law is somehow meaningful binding upon mankind hold to a doctrine of theonomy (and thus are theonomists), the most (I believe) compelling form of which is theonomic reconstructionism (a doctrine appearing frequently in reformed theology). To a reconstructionist, the law is separated into ethical and ceremonial/illustrative components (as noted by dann); the former remains binding as principles for civil conduct and ethical life, the latter was binding only upon pre-messiahIsrael. Thus, while a Christian is free (as argued very persuasively by dann above) to walk afoul of the entirety of the Mosaic law without consequences as to his eternal salvation, he may be positioning himself in opposition to the civiljudgement of God1, which could lead to his experience of this present life being rather badly fouled up.

1 Another way to think of this is through the lens of what are called spiritual laws; this is the notion that God's ethical laws have material consequences, in the form of biases or "drifts" in the natural situational order. For example, tit for tat is a spiritual law of rabbinic origin which basically says "what goes around comes around" or (in more Christian terms) "God is not mocked - as a man sows, so shall he reap."

Under the Mosaic religion, especially the Talmudic version that is the basis for all Orthodox Judaism, Judaic law does not apply to non-Jews in any case, even those who accept that the Jewish religion is entirely correct. In essence, the Jewish religion believes that Hebraic law is the result of a covenant between the Jews and God as the God's chosen people; the Jewish legends actually claim that God chose a number of other, more powerful peoples first, but none of them were willing to accept the entire law, whereas the Jews, when offered the law, said, "we will obey and we will hear", implying that they would first agree to obey and only afterwards inquire as to what the law actually said.

That having been said, the Jewish position is that non-Jews, as non-signatories, are not bound by the special laws which bind Jews in general; they are rather bound by the Noachide covenant. In Israel, there are actually a small number of philosemites who believe in the one god and the Old Testament but do not keep all of Jewish law but rather only the Noachide laws; and most people who request conversion are told that it is in their interests to keep only the Noachide law rather than accept the burden of the entire Jewish legislation, and only allowed to convert if they insist.

Jesus' mission was originally limited only to Jews. According to Matthew he agreed to save the gentiles after an old woman came to have her child healed, and, upon Jesus telling her that he was sent only for Jews, she begged him to help her, claiming that "Even the dogs are allowed to eat the scraps that fell from the Jewish table". Jesus than realized that "her faith was great" and expanded his mission to include all the people's of the world. The New Testament contains within it, the stress of a philosophy that was originally tied to Jewish exceptionalism and then became a universal faith. The early Christians were good Jews; Jesus himself called the Jewish temple "his father's house" (despite no mention of temple sacrifices being necessary in the New Testament) and the Last Supper was almost certainly the Feast of Passover. The claim could be made that the need to obey Old Testament law ended only with the sacrifice of Jesus, but this seems a little specious considering that Jesus himself upheld the law.

If he upheld the law, where is the conflict coming from? Mainly from the fact that Jesus was one of the world's great spiritual reformers, one of a series of people in all culture and all times who refined a civilization in order to make it more human, equitable, and kind. The Law for instance, mandates stoning for a woman caught in adultery. Jesus does NOT say "Don't stone her for we are in a new era of love, etc.", but rather, "Let he without sin cast the first stone." This criticism has to do with the essential inequity of people casting stones to kill an adulturer when they themselves are "guilty in their thoughts of using her for that same thing they wish to stone her for"; it's not an attack on all law in general. He attacks a specific aspect of the law, and not the law itself.

Interestingly, Rabinnic Judaism was coming to many of the same conclusions at the time, but within a more conservative framework. Much like a modern New York lawyer, the Rabbis were twisting the word of god to serve an essentially humanistic and egalitarian vision. For instance, the Bible clearly mandates the death penalty for a rebellious child. By the time the Talmud is done with this rule, said rebellious child must exactly resemble his father and mother, read a certain formula word for word, and spit at both his parents in the presence of two witnesses who have warned him not to do so three times beforehand. Obviously, not something that would happen in day to day life.

Over time, this viewpoint of Rabbinic Judiasm became more explicit. For instance, Hillel, one of the great Rabinnic teachers, specifically states, "Do unto others as you would have them do unto you. That is the whole law. The rest is just commentary." Since Hillel and Jesus were contemporaries, it is impossible to say who said this first. The difference between Judaism and Christianity is that, since Christianity believes these words came from the son of god, it had the effect of undoing all contradictory statements, whereas Hillel's statement has the effect of a legal opinion by a respected, but nevertheless human, judge.

The reason I am bringing this up is because Christianity, if it is not to be antinominian, must have its own laws; ask any Christian, from any sect. Each will have their own internal views of how God is to be served. So does Judaism. At the end of the day, the fight between the view of legality and love within the heart is to be found within all religions, whether they make the conflict explicit, as in Christiaity or Judaism, which does not. Do we really need to base the belief that only love and humanity is important on the words of anyone, or do we find this truth in all cultures and all times in some secret place deep within our heart?